Correct Answer
B — −20 VThe dependent source evaluates to −30 V and the series 10 V source gives a net branch voltage of −20 V.
What This Question Is Really Testing
This is a sign-convention question involving a current-controlled dependent voltage source and KVL. The important point is to keep the negative sign of the controlling current and then combine source voltages according to the polarity marks shown in Fig. Q6.
Concept Foundation
A diamond-shaped source is a dependent source. Its value is determined by another circuit variable. Here the source voltage is vx = 15i2. The +/− marks define the reference polarity. If the calculated source voltage is negative, the actual polarity is opposite to that reference; the negative sign must not be discarded.
Step 1 — Evaluate the Dependent Source
Use the controlling current exactly as given, including its sign.
i2 = −2 A
vx = 15i2
vx = 15(−2) = −30 V
Step 2 — Relate the Two Series Source Voltages
The branch voltage v is measured from the upper + reference to the lower − reference. Both source reference polarities are shown + at the top and − at the bottom, so their signed voltages add.
Step 3 — Substitute and Simplify
Therefore the correct option is B.
Why This Method Works
KVL uses algebraic source voltages, not just magnitudes. A negative value of vx automatically accounts for the actual polarity being opposite to the marked reference.
Independent Verification / Cross-Check
Bottom → top rise = 10 + (−30) = −20 V
The same signed sum reproduces the requested branch voltage, confirming the result.
Concept Extension
- A dependent source remains active during normal circuit analysis.
- Its value must first be written in terms of the controlling current or voltage.
- Negative controlled-source values are physically valid and indicate reversed actual polarity.
Exam Strategy
For dependent-source MCQs: evaluate the controlling expression first → keep its sign → then apply KVL/KCL. Never replace a signed current by its magnitude.
